Watch at the rotation on the right. The wheel defined by
the dark-bright sectors is rotating clockwise and the spokes are rotating counter-clockwise?

Look
again… The spokes stay put! Rather, each spoke makes a tiny shift in one direction and then slowly (subliminally) moves back.

What to do

Watch the rotation for a while with a steady gaze, then stop it, and observe that the illusory motion has caused a motion aftereffect.

You can change the speed (with buttons), the spoke colour and the the gray-modulation depth of the sectors with the slider. With most colours the spoke-motion does not occur. The illusory motion is still evoked with very low contrast.

Comment

When one analyses step-by-step the gray levels next to the spokes, there are two steps where any given spoke first merges with the preceding sector on one side, then with the succeeding sector. Since in this transition the spoke’s identity is lost and thus it (seemingly) changes position, it is seen as moving. In addition, there is a Gestalt factor at play: each individual spoke only moves one single tiny step per rotation of the sectors, but each one does so at a different time. Since all spokes are grouped together, the entire spoke wheel is perceived as undergoing a continuous rotation.
Update 2011-11-24: there is now a paper by Anstis & Rogers (see below) that enlarges on the explanation.

We use the motion aftereffect in combination with EEG recordings as a tool to analyse the
human motion system (motion publications).

Sources

Invented by Anstis & Rogers in 2001. I saw it
at the ARVO 2001, and it impressed me so much that I programmed the first version of this demonstration on that very evening.